We perform several experiments under above architecture setting and traversal way to show the disentanglement quality on MNIST datasets. The disentanglement quantitative results of comparing with \(\beta \) -VAE [1]}, FactorVAE [2]} and Guided-VAE [3]} are presented in Fig REF . Here, considering the dimension of the representation and the number of parameters, other works' bottleneck size is set to 12, i.e., \(d(z)=12\) . This setting helps reduce the impact of differences in complexity between model frameworks. However, for a better comparison, we only select seven dimensions that change more regularly. In our model, we change the three-block representation \(\lbrace s^i\rbrace _{i=1}^3\)  and then the rest representation \(c^3\)  changes according to two dimensions as a whole, i.e., \(c^3=(c^3_{1:2},c^3_{3:4},c^3_{5:6},c^3_{7:8})\) .
And Fig REF  shows that \(\beta \) -VAE hardly ever gets a worthwhile disentangled representation, but FactorVAE appears to attribute change as representation varies. Moreover, Fig REF  and Fig REF  both show great disentangled images, with \(h_1\)  changing in Guided-VAE and \(s^1\)  changing in BHiVAE, the handwriting is getting thicker, and \(h_3,s^2\)  control the angle of inclination. These all demonstrate the model capabilities of our model.
<TABLE>